"Benford's Law can be used to show that binary is the best base for doing floating point math."<p><a href="http://blogs.msdn.com/b/ericlippert/archive/2005/01/13/floating-point-and-benford-s-law-part-two.aspx" rel="nofollow">http://blogs.msdn.com/b/ericlippert/archive/2005/01/13/float...</a>
>In the United States, evidence based on Benford's Law has been admitted in criminal cases at the federal, state, and local levels.<p>This, to me, is the most interesting part of the article.
It is very surprising that distributions such as Fibonacci and the powers of two follow this law. Some number sequences that don't are numbers like pi and e. These numbers are said to be normal numbers, meaning they have an equal distribution amongst all digits. However, this hasn't been rigorously proven and is still an open problem.[1]<p><a href="http://en.m.wikipedia.org/wiki/Normal_number" rel="nofollow">http://en.m.wikipedia.org/wiki/Normal_number</a>
I worked at a hedge fund and we used this to figure out whether other funds were falsifying their returns or not. The most notable deviation was Bernie Madoff's.
Benford's law is so well known today, that many a "forger" will evade it easily. One way is to create random numbers and find a solution that fits both your goal and Benford's law.<p>I think this is what the German ADAC did when they falsified test results around a general "idea" what they wanted to see.
Terry Tao has written an excellent (if mathematically advanced) post on Benford's law that is worth looking at for a more rigorous presentation.<p><a href="http://terrytao.wordpress.com/2009/07/03/benfords-law-zipfs-law-and-the-pareto-distribution/" rel="nofollow">http://terrytao.wordpress.com/2009/07/03/benfords-law-zipfs-...</a>
Probably the best explanation of the intuition behind Benford's law. Worth a watch if you've got the time:<p><a href="https://www.youtube.com/watch?v=XXjlR2OK1kM" rel="nofollow">https://www.youtube.com/watch?v=XXjlR2OK1kM</a>
To reuse an old post:<p>> [I]t has to do with relative growth/shrinkage and the base of the positional-numbering system you're using. If you have a random starting value (X) multiplied by a second random factor (Y), most of the time the result will start with a one.<p>> You're basically throwing darts at logarithmic graph paper! The area covered by squares which "start with 1" is larger than the area covered by square which "start with 9".
Here's a site a friend and I built a while back to test some open datasets against Benford's Law:<p><a href="http://www.testingbenfordslaw.com/" rel="nofollow">http://www.testingbenfordslaw.com/</a><p>Most seem to match fairly closely. We accept pull requests with new datasets if anyone wants to contribute.
Here's a fairly recent link about using Benford's law to detect fraud.<p><a href="http://www.theregister.co.uk/Print/2014/05/14/theorums_1_benford/" rel="nofollow">http://www.theregister.co.uk/Print/2014/05/14/theorums_1_ben...</a>